A functiony =f(x) is represented parametrically as following
`x=phi(t)=t^(5)-20t+7`
`y=psi(t)=4t^(3)-3t^(2)-18t+3`
where t in [-2,2]
Find the intervals of monotonicity and also find the points of extreama.Also find the range of function.

Explanation

We have `x=phi(t)=t^(5)-5t^(3)-20t+7`
`y=Psi(t)=12t^(2)-6t-187=6(t+1)(2t-3)`
`(dy)/(dx)=(dy//dt)/(dx//dt)=(6(t+1)(2t-3))/((t-2)(t+2)(t^(2)+1))`
Sign scheme of `(dy)/(dx)`write is as follows:

`(dy)/(dx)gt0` for t in `(-1,3//2)`,where y = f(x) increases
`(dy)/(dx)lt0` for t in `[-2,-1)cup (3//2,2]` where y=f(x) decreases.
Also, t=-1 is point minima and `t=3//2` is point of maxima.
Now `psi(-2)=(-2)^(3)=4(-2)^(2)-18(-2)+3=-5`
`psi(2)=4(2)^(3)-3(2)^(2)-18(2)+3=-5`

`psi(2)=4(2)^(3)-3(2)^(2)-18(2)+3=-13`
`psi(-1)=4(-1)^(3)-3(-1)^(2)-18(-1)+3=14`